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Question From class 11 Chapter PARABOLA

Let the curve C be the mirror image of the parabola with respect to the line . If A and B are the points of intersection of C with the line , then the distance between A and B is





Answer :


Solution :

The image of a point in the line mirror is the point (x, y) given by <br> <br> The image of O(0, 0), P(1, 2) and Q(1, -2) in the line mirror x+y+4=0 are O'(-4, -4), A(-4, -5), and B(-2, -5) respectively. Thus, y = -5 is the image of the latusretum PQ in the lien mirror x+y+4=0. <br> Hence, AB=PQ=4 <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/RDS_MATH_V01_C24_S01_190_S01.png" width="80%">

The equation of the image of the curve with respect to the line , is
Find the image of the point (2,1) with respect to the line mirror
Statement 1: The point of intersection of the tangents at three distinct points on the parabola can be collinear. Statement 2: If a line does not intersect the parabola then from every point of the line, two tangents can be drawn to the parabola.
If be any line passing through the intersection of the lines and ,then
A straight line cuts the x-axis at point and y-axis at point B, such that C is middle point of is a mirror image of point B with respect to line is a mirror image of point with respect to line then the ratio of the areas of triangles ' is equal to
Let be a variable chord of parabola which cuts the parabola at A and . If normal at A and B meet at C, then locus of c may be (A) (B) (C) (D)
The area enclosed between the curve and the line is (A) (B) (C) (D)
Let and L : y = 2x be three curves P be a point on C and PL be the perpendicular to the major axis of ellipse E. PL cuts the ellipse at point M. <br> IF R is the point of intersection of the line L with the line
The angle between the lines joining the origin to the points of intersection of the line and the curve is
Let be the image or reflection of the curve about the line mirror . Suppose P be any point on the curve and Q be the image about the line mirror L=0, then Q will lie on . Let the given curve be line mirror L : ax + by + c = 0 . We take a point P on the given curve in parametric form. Suppose Q be the image or reflection of point P about line mirror L=0 which again contains the same = 0 and parameter. Let where t is a parameter. Now let and Eliminating t, we get the equation of the reflected curve .Then answer the following questions. The image of the parabola in the line x+y=a is
If is the reflection of parabola about the line
A variable chord PQ of the parabola is down parallel to the line . If the parameters of the points P & Q on the parabola be p and q respectively then is equal to:
and are the points of intersection of the line and the curve . , is the origin. The lines and are at right angles if
Find the equation of the lines joining the origin to the points of intersection of the line with the curve and show that they are at right angles
Let F be the foot of perpendicular and I be the image of the point (2, -3) with respect to the line 4x - 3y + 8 = 0 respectively, then the mid-point of line segment FI is (a)-4 (c) 4, 2)

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